The technique of combining multiple votes to enhance the quality of a decision is the core of boosting algorithms in machine learning. In particular, boosting provably increases decision quality by combining multiple weak learners-hypotheses that are only slightly better than random guessing-into a single strong learner that classifies data well. There exist various versions of boosting algorithms, which we improve upon through the introduction of QuantumBoost. Inspired by classical work by Barak, Hardt and Kale, our QuantumBoost algorithm achieves the best known runtime over other boosting methods through two innovations. First, it uses a quantum algorithm to compute approximate Bregman projections faster. Second, it combines this with a lazy projection strategy, a technique from convex optimization where projections are performed infrequently rather than every iteration. To our knowledge, QuantumBoost is the first algorithm, classical or quantum, to successfully adopt a lazy projection strategy in the context of boosting.
The technique of combining multiple votes to enhance the quality of a decision is the core of boosting algorithms in machine learning. In particular, boosting provably increases decision quality by combining multiple weak learners-hypotheses that are only slightly better than random guessing-into a single strong learner that classifies data well. There exist various versions of boosting algorithms, which we improve upon through the introduction of QuantumBoost. Inspired by classical work by Barak, Hardt and Kale, our QuantumBoost algorithm achieves the best known runtime over other boosting methods through two innovations. First, it uses a quantum algorithm to compute approximate Bregman projections faster. Second, it combines this with a lazy projection strategy, a technique from convex optimization where projections are performed infrequently rather than every iteration. To our knowledge, QuantumBoost is the first algorithm, classical or quantum, to successfully adopt a lazy projection strategy in the context of boosting.
Boosting is a general method to convert a weak learner (which generates hypotheses that are just slightly better than random) into a strong learner (which generates hypotheses that are much better than random). Recently, Arunachalam and Maity gave the first quantum improvement for boosting, by combining Freund and Schapire's AdaBoost algorithm with a quantum algorithm for approximate counting. Their booster is faster than classical boosting as a function of the VC-dimension of the weak learner's hypothesis class, but worse as a function of the quality of the weak learner. In this paper we give a substantially faster and simpler quantum boosting algorithm, based on Servedio's SmoothBoost algorithm.
Abstract Boosting is an ensemble learning method that converts a weak learner into a strong learner in the PAC learning framework. The AdaBoost algorithm is a well-known classical boosting algorithm for weak learners with binary hypotheses. Recently, Arunachalam and Maity presented the first quantum boosting algorithm by quantizing AdaBoost. Their algorithm, which we refer to as QAdaBoost hereafter, is a quantum adaptation of AdaBoost and only works for the binary hypothesis case. QAdaBoost is quadratically faster than AdaBoost in terms of the VC dimension of the hypothesis class of the weak learner. However, QAdaBoost is polynomially worse in the bias of the weak learner. In this work, we address an open question by Izdebski et al. on the existence of boosting algorithms for quantum weak learners with non-binary hypotheses. We answer this question in the affirmative by developing the QRealBoost algorithm motivated by the classical RealBoost algorithm. The main technical challenge was to provide provable guarantees for convergence, generalization bounds, and quantum speedup, given that quantum subroutines are noisy and probabilistic. We prove that QRealBoost retains the quadratic speedup of QAdaBoost over AdaBoost and further achieves a polynomial speedup over QAdaBoost in terms of both the bias of the learner and the time taken by the learner to learn the target concept class. Finally, we perform empirical evaluations on QRealBoost and report encouraging observations on quantum simulators by benchmarking the convergence performance of QRealBoost against QAdaBoost, AdaBoost, and RealBoost on a subset of the MNIST dataset and Breast Cancer Wisconsin dataset.
Suppose we have a weak learning algorithm A for a Boolean-valued problem: A produces hypotheses whose bias γ is small, only slightly better than random guessing (this could, for instance, be due to implementing A on a noisy device), can we boost the performance of A so that A's output is correct on 2/3 of the inputs? Boosting is a technique that converts a weak and inaccurate machine learning algorithm into a strong accurate learning algorithm. The AdaBoost algorithm by Freund and Schapire (for which they were awarded the Gödel prize in 2003) is one of the widely used boosting algorithms, with many applications in theory and practice. Suppose we have a γ-weak learner for a Boolean concept class C that takes time R(C), then the time complexity of AdaBoost scales as VC(C)⋅poly(R(C),1/γ), where VC(C) is the VC-dimension of C. In this paper, we show how quantum techniques can improve the time complexity of classical AdaBoost. To this end, suppose we have a γ-weak quantum learner for a Boolean concept class C that takes time Q(C), we introduce a quantum boosting algorithm whose complexity scales as VC(C)⋅poly(Q(C),1/γ); thereby achieving a quadratic quantum improvement over classical AdaBoost in terms of VC(C).
Over the last couple of decades, there has been a significant evolution in machine learning (ML) and it has gained much popularity, as the volume of data grows exponentially and the adoption of ML algorithms brings new perspectives, trends, and patterns on the data which help in the process of decision making in businesses. Machine learning has transformed the way technical experts work; on the other hand, quantum computing is also becoming prevalent: a fast-growing technology that takes advantage of the laws of quantum mechanics to solve large problems which might be too complex for a classical computer to solve. Tech giants like IBM and Google have already built the first wave of quantum computers. Many research organizations, governments and universities are investing funds and researching in quantum computing, as quantum computers are expected to bring revolutionary changes and accelerate outcomes in various fields such as drug discovery, electronic materials, fertilizers, artificial intelligence (AI), and so on. A new initiative for research into the potential of quantum computers to expedite the learning process of ML algorithms has been inspired by different applications of machine learning and the possibilities of quantum computing. Multiple factors exist in the environment which can affect the performance and accuracy of quantum computers. The Earth’s magnetic field can have an impact on quantum computers since they are susceptible to noise, such as Wi-Fi or mobile phone radiation. Likewise, weak machine learning algorithms can produce inaccurate results; their predictions similar to mere human guessing. Applying machine learning algorithms in quantum computers achieves speedup in the learning process. A weak inaccurate algorithm can be improved by an accurate machine learning algorithm accompanied by boosting. The interplay or trade-off between noisy quantum computers and quantum machine learning algorithms is an interesting research field to explore. For example, assume A is a quantum machine learning (QML) algorithm with a theoretically excellent performance. However, A’s performance is poor when used with a noisy quantum computer; this is because only slightly more than half of the inputs result in A’s output being correct. Can we make A perform better, so that its output is correct on two-thirds of the inputs? Boosting algorithms work on this aspect.
In the noisy intermediate-scale quantum (NISQ) era, the capabilities of variational quantum algorithms are greatly constrained due to a limited number of qubits and the shallow depth of quantum circuits. We may view these variational quantum algorithms as weak learners in supervised learning. Ensemble methods are general approaches to combining weak learners to construct a strong one in machine learning. In this paper, by focusing on classification, we theoretically establish and numerically verify a learning guarantee for quantum adaptive boosting (AdaBoost). The supervised-learning risk bound describes how the prediction error of quantum AdaBoost on binary classification decreases as the number of boosting rounds and sample size increase. We further empirically demonstrate the advantages of quantum AdaBoost by focusing on a 4-class classification. The quantum AdaBoost not only outperforms several other ensemble methods, but in the presence of noise it can also surpass the ideally noiseless but unboosted primitive classifier after only a few boosting rounds. Our work indicates that in the current NISQ era, introducing appropriate ensemble methods is particularly valuable in improving the performance of quantum machine learning algorithms.
Ensemble learning algorithms, especially Boosting, have achieved remarkable success in classification tasks by combining multiple weak classifiers-you know, the sort that aren’t all that strong by themselves but work real well when you put them together-though traditional methods like AdaBoost? They’re prone to overfitting in noisy datasets, see? Like when a few labels are off or the data has random little glitches, they end up fitting that noise too hard instead of the real pattern, and methods like QBoost-the ones that use quantuminspired optimization, right?-they usually run into two problems: picking the right weak classifiers and just not being very fast computationally, so this study? We propose an optimized QBoost version plus a new way to build weak classifiers, just to fix those issues we mentioned, and the weak classifiers here? We made them based on decision stumps but added adaptive feature weighting, and that weighting part, by the way, helps make the weak classifiers more diverse and better at telling different classes apart, while as for the QBoost framework itself? We tweaked the objective function-threw in a regularization term, yeah?-to balance two things: getting solid classification accuracy and not letting the model get too complex, and we also used a gradient-based optimization algorithm to speed up convergence so the model doesn’t take forever to train; now, the experimental results?We tested on MNIST, CIFAR-10, and UCI Credit. The method shows 3.2% higher accuracy than AdaBoost.It cuts training time by 28%. In label-noise settings, the error rate falls by 5.7%.